The evolution of the mass-transfer functions in liquid Yukawa systems
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
The Evolution of the Mass-Transfer Functions in Liquid Yukawa Systems O. S. Vaulina* Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412 Russia *e-mail: [email protected] Received February 19, 2016
Abstract—The results of analytic and numerical investigation of mass-transfer processes in nonideal liquid systems are reported. Calculations are performed for extended 2D and 3D systems of particles that interact with a screened Yukawa-type Coulomb potential. The main attention is paid to 2D structures. A new analytic model is proposed for describing the evolution of mass-transfer functions in systems of interacting particles, including the transition between the ballistic and diffusion regimes of their motion.
DOI: 10.1134/S1063776116070128
described by a relationship that is a special case of the Green–Kubo formula:
1. INTRODUCTION The problems associated with transport processes (diffusion, viscosity, heat conduction, etc.) in systems of interacting particles are of considerable interest in various fields of science, such as hydrodynamics, plasma physics, medicine, biology, as well as polymer physics and chemistry [1–12]. The application of hydrodynamic approaches makes it possible to successfully describe transport processes only with shortorder interactions. The development of approximate models for describing the liquid state of matter is based on two main approaches, one of which (more fundamental) employs general concepts of statistical physics, while the other relies on analogies between a liquid and a solid (saltation theory). For analyzing transport characteristics in systems of interacting particles and for verifying the available approximations, computer simulation of the dynamics of particles with various model potentials for their interaction is used. Transport processes are usually simulated using moleculardynamics methods based on the integration of reversible equations of motion of particles or on the solution of the Langevin equations taking the irreversibility of the processes under investigation into account [1, 6]. Diffusion is the main process of mass transfer, which determines the energy loss (dissipation) in a system of particles and their dynamic characteristics, such as the phase state, the conditions of wave propagation, and the formation of instabilities. In the case of small deviations of the studied system from the statistical equilibrium state, the diffusion coefficient D is
∞
D=
∫ 0
〈V (0)V (t )〉dt , m
(1)
where 〈V(0)V(t)〉 is the autocorrelation function of velocities V of particles, t is the time, and m is the dimensionality of the system. The diffusion coefficient can also be obtained from analysis of the heat transfer of particles through a unit area element of the medium for t → ∞:
D = lim〈(Δ l ) 〉 /(2mt ), 2
(2)
t →∞
where Δl = Δl(t) is the displacement of an individual particle over time t and the angle brackets indicate averaging over the ensemble and over all time intervals of duration t. Relat
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